Question: $z=44i-32$ What are the real and imaginary parts of $z$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $\text{Re}(z)=44i$ and $\text{Im}(z)=-32$ (Choice B) B $\text{Re}(z)=-32$ and $\text{Im}(z)=44$ (Choice C) C $\text{Re}(z)=44$ and $\text{Im}(z)=-32$ (Choice D) D $\text{Re}(z)=-32$ and $\text{Im}(z)=44i$
Solution: Background Complex numbers are numbers of the form $z={a}+{b}i$, where $i$ is the imaginary unit and ${a}$ and ${b}$ are real numbers. [What is the imaginary unit?] The real part of $z$ is denoted by $\text{Re}(z)={a}$. The imaginary part of $z$ is denoted by $\text{Im}(z)={b}.$ Finding the Real and Imaginary Parts of $z$ In this case, $z={44}i-{32}$ is of the form ${b}i+{a}$, where ${a}={-32}$ and ${b}={44}$. Therefore: $\text{Re}(z)={a}={-32}$. $\text{Im}(z)={b}={44}$. Summary $\text{Re}(z)={-32}$ and $\text{Im}(z)={44}$.